2种快速扩弓方式联合前方牵引治疗青少年骨性Ⅲ类错效果的三维有限元分析

doi:10.3969/j.issn.1674-8115.2024.11.009

上海交通大学学报（医学版） ›› 2024, Vol. 44 ›› Issue (11): 1422-1432.doi: 10.3969/j.issn.1674-8115.2024.11.009

• 论著 · 临床研究 • 上一篇

2种快速扩弓方式联合前方牵引治疗青少年骨性Ⅲ类错效果的三维有限元分析

韩磊(), 鲁桐, 朱培香, 李煌()

南京大学医学院附属口腔医院·南京市口腔医院口腔正畸科，南京大学口腔医学研究所，南京 210008

收稿日期:2024-03-01 接受日期:2024-09-27 出版日期:2024-11-28 发布日期:2024-11-28
通讯作者: 李煌 E-mail:pinedream@163.com;lihuang76@nju.edu.cn
作者简介:韩　磊（1983—），男，副主任医师，博士；电子信箱：pinedream@163.com。
基金资助:
南京市医学科技发展资金资助项目(ZKX23055);南京大学医学院附属口腔医院“3456”育才计划(2022)

Effects of two rapid expansion methods combined with protraction on the treatment of skeletal class Ⅲ malocclusion in adolescents: a three-dimensional finite element analysis

HAN Lei(), LU Tong, ZHU Peixiang, LI Huang()

Department of Orthodontics, Nanjing Stomatological Hospital, Medical School of Nanjing University; Institute of Stomatology, Nanjing University, Nanjing 210008, China

Received:2024-03-01 Accepted:2024-09-27 Online:2024-11-28 Published:2024-11-28
Contact: LI Huang E-mail:pinedream@163.com;lihuang76@nju.edu.cn
Supported by:
Nanjing Health Development Key Project(ZKX23055);“3456” Cultivation Program of Nanjing Stomatological Hospital, Medical School of Nanjing University(2022)

摘要/Abstract

摘要：

目的·应用三维有限元分析法比较骨支抗式和牙支持式快速扩弓联合前方牵引对颅颌面骨缝、骨骼点、骨骼及上颌牙列的作用效果，以指导临床上选择合适的牵引方式及位置。方法·选取一名替牙列期骨性Ⅲ类错伴上颌发育不足的青少年的锥形束计算机断层扫描（cone beam computed tomography，CBCT）影像，建立上颌复合体的三维有限元模型（包括颅颌面骨缝、骨骼点、骨骼及上颌牙列），并在此基础上分别建立骨支抗式、牙支持式快速扩弓联合前方牵引三维有限元模型，而后将前述模型组装成为上颌复合体和骨支抗式快速扩弓联合前方牵引三维有限元模型（模型1）、上颌复合体和牙支持式快速扩弓联合前方牵引三维有限元模型（模型2）。依次根据扩弓方式、牵引位置的不同，在模型1、2中分别建立以下工况：① 根据扩弓方式，将模型1设置为A组，模型2设置为B组。② 根据牵引位置，将上述2组继续分为试验组Ⅰ组（牵引钩位于双侧尖牙颊侧）、Ⅱ组（牵引钩位于双侧第一前磨牙颊侧）和Ⅲ组（牵引钩位于双侧第二前磨牙颊侧）。同时，分别将A、B组中不联合前方牵引设置为对照组（即为A0组、B0组）。采用图表分析的方法对A、B组在不同牵引位置时的颅颌面骨缝应力分布特征，以及颅颌面骨骼点、颅颌面骨骼及上颌牙列的位移趋势进行分析。结果·在颅颌面骨缝应力分布特征方面，A、B组中翼突上颌缝的等效应变最大，且随着牵引位置的后移其等效应变均逐渐增加；AⅠ组各骨缝的最大主应变大于BⅠ组。在颅颌面骨骼位移趋势方面，随着牵引位置的后移，在水平向上A、B试验组的鼻骨和上颌骨均向右移动且位移趋势逐渐减小，在矢状向上该2组的鼻骨均向后移动且位移趋势均减小、上颌骨均向前移动且位移趋势均增大，在垂直向上该2组的鼻骨均向下移动且位移趋势逐渐减小、上颌骨均向上移动且位移趋势逐渐减小。在颅颌面骨骼点（ANS、PNS）位移趋势方面，A组中上颌平面（ANS-PNS平面）发生顺时针旋转，且随着牵引位置的后移该平面顺时针旋转趋势减小；而B组中ANS-PNS平面发生逆时针旋转，且随着牵引位置的后移该平面逆时针旋转趋势更加明显。在上颌牙列位移趋势方面，A、B试验组的中切牙在水平向、矢状向、垂直向上的位移均为负值，即存在远中、唇向、伸长的位移趋势，第一磨牙在水平向上的位移均为负值，即存在颊向位移趋势；且随着牵引位置的后移，中切牙牙冠的唇向移动趋势增大，第一磨牙牙冠从远中移动变为近中移动。结论·临床上前方牵引位置放于后侧有利于上颌骨前移；骨性Ⅲ类错青少年患者可选择不同的扩弓方式联合前方牵引，在实现上颌骨前移的同时实现上颌平面的有利旋转。

关键词: 骨支抗式快速扩弓, 牙支持式快速扩弓, 前方牵引, 三维有限元分析, 骨性Ⅲ类错

Abstract:

Objective ·To compare the effects of bone-anchored rapid expansion and tooth-borne rapid expansion combined with protraction on craniofacial sutures, skeletal points, bones and maxillary dentition using three-dimensional finite element analysis, and provide guidance for the clinical selection of appropriate traction methods and sites. Methods ·A cone beam computed tomography (CBCT) image of one adolescent with skeletal class Ⅲ malocclusion and maxillary hypoplasia during the mixed dentition period was selected to establish a three-dimensional finite element model of the maxillary complex (including craniofacial sutures, skeletal points, bones and maxillary dentition). Based on this, the three-dimensional finite element models of bone-anchored and tooth-borne rapid expansion combined with protraction were respectively established. Then, the aforementioned models were assembled into a three-dimensional finite element model of maxillary complex with bone-anchored rapid expansion combined with protraction (Model 1), and a three-dimensional finite element model of maxillary complex with tooth-borne rapid expansion combined with protraction (Model 2). According to the different expansion methods and protraction sites, the following conditions were set up: ① Based on the expansion methods, Model 1 was set as Group A, and Model 2 was set as Group B. ② Based on the protraction sites, Group A and B were further divided into experimental group Ⅰ(protraction hooks were placed buccally on both sides of the maxillary canines), experimental group Ⅱ(protraction hooks were placed buccally on both sides of the maxillary first premolars) and experimental group Ⅲ (protraction hooks were placed buccally on both sides of the maxillary second premolars), respectively. Additionally, as a control, Group A0 used bone-anchored rapid expansion alone without protraction, while Group B0 used tooth-borne rapid expansion without protraction. The stress distribution characteristics of craniofacial sutures in groups A and B at different protraction sites, as well as the displacement trends of craniofacial skeletal points, craniofacial bones and maxillary dentition were analyzed by using charts and tables. Results ·In terms of stress distribution characteristics of craniofacial sutures, pterygomaxillary suture′s equivalent strain was maximal in both groups A and B, and it increased when protraction hooks were placed backwards. The maximum principal strain value of each suture in Group AⅠ was larger than that in Group BⅠ. In terms of the displacement trend of craniofacial bones, as the protraction sites shifted posteriorly, both the nasal bones and maxilla in the horizontal direction moved rightward with decreasing displacement trends in both groups A and B. In the sagittal direction, the nasal bones moved posteriorly with decreasing displacement trends, while the maxilla moved anteriorly with increasing displacement trends in groups A and B. In the vertical direction, the nasal bones moved downward with decreasing displacement trends, and the maxilla moved upward with decreasing displacement trends in groups A and B. In terms of displacement trends of craniofacial skeletal points (ANS, PNS), the maxillary plane (ANS-PNS plane) in Group A underwent clockwise rotation, with the clockwise rotation trend decreasing as the protraction sites shifted posteriorly, while the maxillary plane (ANS-PNS plane) in Group B underwent counterclockwise rotation, with the counterclockwise rotation trend becoming more apparent as the protraction sites shifted posteriorly. In terms of the displacement trend of the maxillary dentition, the displacement of the central incisors in the horizontal, sagittal and vertical directions in the experimental groups A and B was all negative, presenting a tendency to move distally, labially and extrusively. The displacement of the first molar in the horizontal direction was also negative, indicating a trend of buccal displacement. Additionally, as the protraction site shifted posteriorly, the labial movement trend of the central incisors′ crown increased, and the crowns of the first molars changed from mesial to distal movement. Conclusion ·Clinically, placing protraction sites posteriorly is beneficial for the anterior movement of the maxilla. Adolescent with skeletal class Ⅲ malocclusion can choose different rapid expansion with protraction to achieve maxillary anterior displacement while realizing favorable rotation of maxillary plane.

Key words: bone-anchored rapid expansion, tooth-borne rapid expansion, protraction, three-dimensional finite element analysis, skeletal Class Ⅲ malocclusion

中图分类号:

R783.5

韩磊, 鲁桐, 朱培香, 李煌. 2种快速扩弓方式联合前方牵引治疗青少年骨性Ⅲ类错效果的三维有限元分析[J]. 上海交通大学学报（医学版）, 2024, 44(11): 1422-1432.

HAN Lei, LU Tong, ZHU Peixiang, LI Huang. Effects of two rapid expansion methods combined with protraction on the treatment of skeletal class Ⅲ malocclusion in adolescents: a three-dimensional finite element analysis[J]. Journal of Shanghai Jiao Tong University (Medical Science), 2024, 44(11): 1422-1432.

图/表 13

表1 模型1和模型2中各种材料的杨氏模量与泊松比

Tab 1 Young′s modulus and Poisson′s ratio of various materials in Model 1 and Model 2

Material	Young′s modulus/(N·mm^-2)	Poisson′s ratio
Craniofacial bones	13 400	0.30
Sutures	70	0.40
Maxillary dentition	20 700	0.30
Expander	190 000	0.33
Microimplant	113 000	0.33

图1 模型1和模型2的8个工况设置Note： Red arrows represent traction sites and directions.

Fig 1 Eight conditions of Model 1 and Model 2

图2 模型的观测对象的示意图Note： A. Anterior aspect of the model. B. Inferior aspect of the model. a—frontal bone; b—maxilla; c—zygomatic bone; d—nasal bone; e—ANS; f—PNS; g—nasofrontal suture; h—zygomaticomaxillary suture; i—zygomatic temporal suture; j—zygomatic frontal suture; k—pterygomaxillary suture; l—nasal suture; m—nasomaxillary suture; n—maxillary central incisors; o—maxillary first molars.

Fig 2 Schematic diagram of observation objects of the model

图3 上颌复合体三维有限元模型和2种快速扩弓联合前方牵引三维有限元模型图示Note： A. Three-dimensional finite element model of maxillary complex. B. Three-dimensional finite element model of bone-anchored rapid expansion with protraction. C. Three-dimensional finite element model of tooth-borne rapid expansion with protraction.

Fig 3 Diagram of the three-dimensional finite element model of maxillary complex and two rapid expanders with protraction

图4 模型1（A）及模型2（B）图示

Fig 4 Diagram of Model 1 (A) and Model 2 (B)

图5 骨支抗式扩弓联合前方牵引（A）和牙支持式扩弓联合前方牵引（B）的试验组与对照组骨缝等效应变的比值

Fig 5 Experimental group-to-control group ratio of sutures′ equivalent strain of bone-anchored rapid expander with protraction (A) and tooth-borne rapid expander with protraction (B)

图6 AⅠ、BⅠ组各骨缝的最大主应变图示（右视图及前视图）Note： A. Pterygomaxillary suture. B. Zygomaticomaxillary suture. C. Zygomatic temporal suture. D. Zygomatic bone. E. Nasomaxillary suture. F. Nasofrontal suture. In scale label, positive value represents tensile stress, and negative value represents compressive stress. Based on the right and frontal views of the nasofrontal suture, which are represented as points and lines with relatively small values, no analysis was conducted on the nasofrontal suture in this area.

Fig 6 Diagram of sutures′ maximum principal strain of Group AⅠ and Group BⅠ (right view and front view)

表2 颅颌面骨骼在 X 轴上的位移/mm

Tab 2 Displacement of the cranio-maxillofacial bones along the X-axis/mm

Cranio-maxillofacial bone	Group A				Group B
Cranio-maxillofacial bone	A0	AⅠ	AⅡ	AⅢ	B0	BⅠ	BⅡ	BⅢ
Frontal bone	-0.063 97	-0.064 05	-0.063 98	-0.063 93	-0.003 08	-0.003 52	-0.002 89	-0.002 24
Maxilla	-0.063 97	-0.064 05	-0.063 98	-0.063 93	-0.003 08	-0.003 52	-0.002 89	-0.002 24
Zygomatic bone	-0.045 22	-0.045 16	-0.045 05	-0.044 98	-0.001 53	-0.001 67	-0.001 33	-0.000 99
Nasal bone	-0.024 05	-0.023 81	-0.023 73	-0.023 71	-0.000 48	-0.000 35	-0.000 16	-0.000 04

表3 颅颌面骨骼在 Y 轴上的位移/mm

Tab 3 Displacement of the cranio-maxillofacial bones along the Y-axis/mm

Cranio-maxillofacial bone	Group A				Group B
Cranio-maxillofacial bone	A0	AⅠ	AⅡ	AⅢ	B0	BⅠ	BⅡ	BⅢ
Frontal bone	0.027 70	0.027 40	0.027 30	0.027 30	0.001 00	0.000 77	0.000 63	0.000 62
Maxilla	-0.008 59	-0.009 51	-0.009 81	-0.010 00	-0.000 61	-0.003 45	-0.003 89	-0.004 34
Zygomatic bone	-0.009 50	-0.009 87	-0.009 98	-0.010 01	-0.000 27	-0.001 05	-0.001 26	-0.001 42
Nasal bone	0.024 60	0.024 40	0.024 25	0.024 21	0.000 93	0.000 77	0.000 56	0.000 37

表4 颅颌面骨骼在 Z 轴上的位移/mm

Tab 4 Displacement of the cranio-maxillofacial bones along the Z-axis/mm

Cranio-maxillofacial bone	Group A				Group B
Cranio-maxillofacial bone	A0	AⅠ	AⅡ	AⅢ	B0	BⅠ	BⅡ	BⅢ
Frontal bone	0.026 51	0.026 10	0.025 80	0.025 70	0.001 10	0.000 64	0.000 32	0.000 31
Maxilla	0.023 89	0.023 40	0.023 20	0.023 10	0.001 05	0.000 36	0.000 18	0.000 11
Zygomatic bone	0.021 34	0.020 90	0.020 80	0.020 70	0.000 70	0.000 36	0.000 20	0.000 10
Nasal bone	-0.018 22	-0.018 00	-0.017 80	-0.017 70	-0.000 70	-0.000 63	-0.000 35	-0.000 07

图7 A组（A）、B组（B）的各骨骼点（ANS、PNS）在垂直向上（ Z 轴）的位移趋势

Fig 7 Displacement trend of each skeletal point (ANS, PNS) in Group A (A) and Group B (B) in the vertical direction (Z-axis)

图8 A、B组上颌中切牙和上颌第一磨牙的三维方向的位移分析Note： A?C. Displacement analysis of maxillary central incisor in the horizontal direction (A), sagittal direction (B) and vertical direction (C). D?F. Displacement analysis of maxillary first molar in the horizontal direction (D) sagittal direction (E) and vertical direction (F).

Fig 8 Three-dimensional displacement analysis of maxillary central incisors and maxillary first molars in Group A and Group B

图9 A、B组的上颌第一磨牙的位移趋势图示Note： The color of the arrow represents the magnitude of displacement, and the direction of the arrow represents the direction of displacement.

Fig 9 Diagram of the displacement trend of the maxillary first molar in Group A and Group B

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2种快速扩弓方式联合前方牵引治疗青少年骨性Ⅲ类错效果的三维有限元分析

Effects of two rapid expansion methods combined with protraction on the treatment of skeletal class Ⅲ malocclusion in adolescents: a three-dimensional finite element analysis

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